id: 05949236
dt: j
an: 2011e.00781
au: Kantrowitz, Robert; Neumann, Michael N.
ti: Let\rq s do launch: More musings on projectile motion.
so: Pi Mu Epsilon J. 13, No. 4, 219-228 (2011).
py: 2011
pu: Worcester Polytechnic Institute (WPI), Mathematical Sciences, Worcester, MA
la: EN
cc: M50 I40
ut: mathematical applications; physics; mechanics; trajectories; maximal
displacement; optimal range; parametric equations; computer algebra;
critical point equation; global maximum; local maximum; completion of a
square; implicit differentiation method
ci:
li:
ab: Summary: This note addresses the motion of a projectile that is launched
from the top of a tower and lands on a certain mountain. The main
problem is to find a manageable formula for the initial angle of
elevation that maximizes the distance the projectile travels. We first
explore the extent to which computer algebra systems are helpful when
applied to the classical critical point approach in this context. We
then show how the shortcomings of this approach can be overcome by
different methods that lead to a surprisingly simple formula for the
best launch angle. As an illustration, optimal home runs for the game
of tee ball are discussed.
rv: